JACKSON, FRANKLIN GAIN P.S.A.L. FINAL

Although Andrew Jackson High School has not won a Public Schools Athletic League basketball title since the mid-1940's, when Bob Cousy played, it has been in the playoffs almost every year in Coach Chuck Granby's 13-year reign. And now it has another chance to win the title, gaining the final yesterday with Benjamin Franklin.

The Hickories posted a 67-55 victory over Forest Hills in the semifinals yesterday at St. John's University in Jamaica, Queens, thanks mostly to 14-year-old Greg (Boo) Harvey. The freshman guard scored a game-high 24 points and showed some of Cousy's ball-handling ability in leading his team to its 20th victory in 24 games.

''Nobody expected us to be here this year,'' said Granby, who has coached Jackson to division championships in Queens 11 times, the citywide quarterfinals four times and the final twice. Last season his team lost in the final to Hamilton.

''We lost seven starters from last year, and both my guards, Boo and Ron Edwards, are ninth graders and weren't even in high school last year,'' he said. ''But when we get to the playoffs, I always ask the players what time is it, and the answer is Jackson time.''

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Jackson got 30 points from its senior front line - 11 by John Hughley, 10 by Mike Gibson and 9 by Kevin Jones. Steve Daniels, a senior guard, led Forest Hills with 19 points. Keith Mason, a sophmore guard, had 17 and John Jennings, senior center, had 16 before fouling out with 13 seconds left. Jackson Takes Over

The score was 15-15 after the first period, as Jennings got 6 points. But with a 17-7 third-quarter spurt, Jackson took control. Forest Hills never got closer than 6 the rest of the way.

In the B Division semifinals, Murry Bergtraum (17-5) and Norman Thomas (20-4) triumphed. Ron Duncan poured in 55 points for Thomas. Bergtraum won by 65-54 from Prospect Heights. Clarence Howard had 17 points for the winners. The game's high scorer, however, was Prospect Heights' Mike Ervin, with 23.

Norman Thomas had an easy time beating the High School of Printing, 80-59. Duncan's total included 11 for 13 free throws. Fred Carty had 19 points and Gerald Coleman 10 for Thomas. Paul Tate led Printing (11-4) with 18.

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A version of this article appears in print on March 8, 1982, on Page C00008 of the National edition with the headline: JACKSON, FRANKLIN GAIN P.S.A.L. FINAL. Order Reprints|Today's Paper|Subscribe